Question: Ishaan is $2$ times as old as Christopher. $35$ years ago, Ishaan was $7$ times as old as Christopher. How old is Christopher now?
Solution: We can use the given information to write down two equations that describe the ages of Ishaan and Christopher. Let Ishaan's current age be $i$ and Christopher's current age be $c$. The information in the first sentence can be expressed in the following equation: ${i = 2c}$ 35 years ago, Ishaan was $i - 35$ years old, and Christopher was $c - 35$ years old. The information in the second sentence can be expressed in the following equation: ${i - 35 = 7(c - 35)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$, it might be easiest to use our first equation for $i$ and substitute it into our second equation. Our first equation is: ${i = 2c}$. Substituting this into our second equation, we get: ${2c} {-35 = 7(c - 35)}$ which combines the information about $c$ from both of our original equations. Simplifying the right side of this equation, we get: $2 c - 35 = 7 c - 245$. Solving for $c$, we get: $5 c = 210.$ $c = 42$.